# How to deal with the connection between symbolic caculations and numerical caculations?

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Cola on 21 Mar 2022
Edited: Cola on 23 Mar 2022
First I need to do symbolic calculations to get the required equations. Then I use the equations for numerical calculations.
For example, I obtain the equation Ge1=-1/((2*s + 1)/(s/20 + 1) + s^2*(s/10 + 1)) by symbolic calculations.
Then If Ge1_1=-1/((2*s + 1)/(s/20 + 1) + s^2*(s/10 + 1)), one can do numerical calculations.
And I can't do numerical calculations when I want Ge1_1=Ge1.
I don't know how to deal with the connection between symbolic caculations and numerical caculations. Is there a way to solve the problem? Thank you for reading and help.
Matlab Code:
syms s
kp=(2*s+1)/(0.05*s+1);
H=1/(s^2*(0.1*s+1));
P12_1=[-1 / H - kp];
Ge1=inv(P12_1)
s=tf('s')
w=logspace(-1,1,1000);
Ge1_1=Ge1;
% Ge1_1=-1/((2*s + 1)/(s/20 + 1) + s^2*(s/10 + 1));
[mag,pha,w]=bode(Ge1_1,w);
##### 2 CommentsShowHide 1 older comment
Cola on 23 Mar 2022
Edited: Cola on 23 Mar 2022
@Walter Roberson Thanks. I mean [-1/H-kp], that is ,[(-1/ H) - kp].

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### Accepted Answer

Torsten on 21 Mar 2022
"matlabFunction" converts symbolic expressions into function handles for numerical calculations.
help matlabFunction
##### 1 CommentShowHide None
Cola on 23 Mar 2022
Edited: Cola on 23 Mar 2022
@Torsten Thank you so much.
Matlab code:
syms s
kp=(2*s+1)/(0.05*s+1);
H=1/(s^2*(0.1*s+1));
P12_1=[-1/H-kp];
Ge1=inv(P12_1);
Ge1 =
omega=logspace(-1,1,1000);
Ge1_0=matlabFunction(Ge1);
Ge1_0 = function_handle with value:
@(s)-1.0./((s.*2.0+1.0)./(s./2.0e+1+1.0)+s.^2.*(s./1.0e+1+1.0))
Ge1_1=abs(Ge1_0(1i*omega));

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### More Answers (1)

Paul on 23 Mar 2022
Of course, the symbolic approach will work and might even have some benefits (IDK), but just want to make sure you're aware that it's not really necessary.
% symbolic approach
syms s
kp=(2*s+1)/(0.05*s+1);
H=1/(s^2*(0.1*s+1));
P12_1=[-1 / H - kp;];
Ge1=inv(P12_1);
[num,den] = numden(Ge1);
Ge1 = num/den
Ge1 =
% control system toolbox functionality
s = tf('s');
kp=(2*s+1)/(0.05*s+1);
H=1/(s^2*(0.1*s+1));
P12_1=[-1 / H - kp;];
Ge1=inv(P12_1);
Ge1 = minreal(Ge1) % normalizes numerator and denominator for comparison to symbolic result, not necessary otherwise
Ge1 = -10 s - 200 ------------------------------------ s^4 + 30 s^3 + 200 s^2 + 400 s + 200 Continuous-time transfer function.
##### 3 CommentsShowHide 2 older comments
Cola on 23 Mar 2022
@Walter Roberson Wow，it is a cool way. I really appreciate your help.

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